Let the time (in hours) needed to repair a broken car be a continuous random variable $X$.
Then, in the case of $a$ and $b$ being two positive numbers and $b$ > $a$, would the following two problems ...

I have a joint probability of a very specific form:
$P(x_1,\cdots,x_n)=\phi(x_1)\psi(x_1,x_2)\phi(x_2)\cdots\psi(x_{n-1},x_n)\phi(x_n)=\prod_{i=1}^n \phi(x_i) \prod_{i=1}^{n-1} \psi(x_i,x_{i+1})$
I ...

at a particular gym, 70% of the members take at least one fitness class and work with a personal trainer. if 18% of the gym members work with a personal trainer, find the probability that a randomly ...

I have read about both conditional and unconditional MLE parameters estimation for ARIMA models but I have problem understanding the concept from the statistical books . Does conditional MLE mean that ...

I'd like to work with a what I believe is a called a "hierarchical process" -- given by the multiplication of a pair of exponential distributions such that the random variable from one process is the ...

Let $q$ be a conditioned pdf over $\mathbf{X}=X_1,\dots,X_n$ binary r.v.s in the form $$q(\mathbf{X})=\begin{cases}q_{0}(\mathbf{X}_{\setminus i}) \text{ if } X_{i}=0\\q_{1}(\mathbf{X}_{\setminus i}) ...

I understand the arithmetic derivation of the PDF of a conditional distribution of a multivariate Gaussian, as explained here, for example. Does anyone know of a more conceptual (perhaps, co-ordinate ...

To start off, I've been reading "Statistics: Principles and Methods" 7th edition by Johnson and Bhattacharyya. I understand the conditional probability formulas and have practiced the examples in the ...

It is well known that of all the joint distributions $p(x,y)$ with fixed marginals $p(x),p(y)$, the one with the highest entropy is:
$$
p(x,y)=p(x)p(y).
$$
Suppose instead that we have conditionals. ...

If you draw 5 cards from a standard deck of 52 cards, then the probability of your hand having the Ace of Spades is:
$$\frac{51\choose 4}{52\choose 5} = \frac{51!5!47!}{4!47!52!} = \frac{5}{52}$$
If, ...

Full disclosure: I've posted this on reddit at /r/askstatistics, but haven't gotten any feedback yet, so I'm re-posting here in the hopes of getting some more exposure. Sorry for the long question.
I ...

I have P(Headache|Stress) = 0.88 where Stress is a "necessary" cause.
Again, I have P(Headache|Coffee) = 0.35 where Coffee is also a "necessary" cause.
Now I want to calculate joint effect of Stress ...

I think that this question is related: Covariance of a compound distribution, but it's too abstract for me (I believe that what I have to do must be simpler).
Here's the given: machines $A$ and $B$ ...

There are two events involved, say event A and event B. I want to know the probability of event B conditioned on the event A. The relation between the two events are as follows. We can not talk about ...

Similar questions have been asked in this context but this one seems a bit different.
[Aim]
We would like to find out what the probability is of a person purchasing a 4USD column D (see below) price ...

What's given:
I have an urn with with a set $S$ of balls where $|S| = N$. Each ball $b_i$ has a unique id and can either be red or blue. There are $m$ red balls in the urn.
$d$ times I randomly draw ...

Given $P(X\perp Y\;|\;Z)$ and $P(X\perp Y\;|\;W)$, prove or disprove that $P(X\perp Y\;|\;Z, W)$
I'm pretty sure this isn't true, as I haven't been able to prove it using Bayes' Theorem and messing ...